Radial Basis Function

A new approach for the segmentation of gland units in histological images is proposed with the aim of contributing to the improvement of the prostate cancer diagnosis. Clustering methods on several colour spaces are applied to each sample in order to generate a binary mask of the different tissue components. From the mask of lumen candidates, the Locally Constrained Watershed Transform (LCWT) is applied as a novel gland segmentation technique never before used in this type of images. 500 random gland candidates, both benign and pathological, are selected to evaluate the LCWT technique providing results of Dice coefficient of 0.85. Several shape and textural descriptors in combination with contextual features and a fractal analysis are applied, in a novel way, on different colour spaces achieving a total of 297 features to discern between artefacts and true glands. The most relevant features are then selected by an exhaustive statistical analysis in terms of independence between variables and dependence with the class. 3.200 artefacts, 3.195 benign glands and 3.000 pathological glands are obtained, from a data set of 1468 images at 10x magnification. A careful strategy of data partition is implemented to robustly address the classification problem between artefacts and glands. Both linear and non-linear approaches are considered using machine learning techniques based on Support Vector Machines (SVM) and feedforward neural networks achieving values of sensitivity, specificity and accuracy of 0.92, 0.97 and 0.95, respectively.

Surface reconstruction from large unorganized data sets is very challenging, especially if the data present undesired holes. This is usually the case when the data come from laser scanner 3D acquisitions or if they represent damaged objects to be restored. An attractive field of research focuses on situations in which these holes are too geometrically and topologically complex to fill using triangulation algorithms. In this work a local approach to surface reconstruction from point-clouds based on positive definite Radial Basis Functions (RBF) is presented that progressively fills the holes by expanding the neighbouring information. The method is based on the algorithm introduced in [7] which has been successfully tested for the smooth multivariate interpolation of large scattered data sets. The local nature of the algorithm allows for real time handling of large amounts of data, since the computation is limited to suitable small areas, thus avoiding the critical efficiency problem involved in RBF multivariate interpolation. Several tests on simulated and real data sets demonstrate the efficiency and the quality of the reconstructions obtained using the proposed algorithm.

Neuro-fuzzy systems based on Radial Basis Function Networks (RBFN) and other hybrid artificial intelligence techniques are currently under intensive investigation. This paper presents a RBFN training algorithm based on evolutionary programming and cooperative evolution. The algorithm alternatively applies basis function adaptation and backpropagation training until a satisfactory error is achieved. The basis functions are adjusted through an error goal function obtained through training and testing of the second part of the network. The algorithm is tested on benchmark data sets. It is applicable to on-line adaptation of RBFN and building adaptive intelligent systems

A study on the applicability of dierent kinds of neural networks for the probabilistic analysis of structures, when the sources of randomness can be modeled as random variables, is summarized. The networks are employed as numerical devices for substituting the ®nite element code needed by Monte Carlo simulation. The comparison comprehends two network types (multi-layer perceptrons and radial basis functions classi®ers), cost functions (sum of square errors and cross-entropy), optimization algorithms (back-propagation, Gauss±Newton, Newton±Raphson), sampling methods for generating the training population (using uniform and actual distributions of the variables) and purposes of neural network use (as functional approximators and data classi®ers). The comparative study is performed over four examples, corresponding to dierent types of the limit state function and structural behaviors. The analysis indicates some recommended ways of employing neural networks in this ®eld. Ó

A multi-fidelity (MF) active learning method is presented for design optimization problems characterized by noisy evaluations of the performance metrics. Namely, a generalized MF surrogate model is used for design-space exploration, exploiting an arbitrary number of hierarchical fidelity levels, i.e., performance evaluations coming from different models, solvers, or discretizations, characterized by different accuracy. The method is intended to accurately predict the design performance while reducing the computational effort required by simulation-driven design (SDD) to achieve the global optimum. The overall MF prediction is evaluated as a low-fidelity trained surrogate corrected with the surrogates of the errors between consecutive fidelity levels. Surrogates are based on stochastic radial basis functions (SRBF) with least squares regression and inthe-loop optimization of hyperparameters to deal with noisy training data. The method adaptively queries new training data, selecting b...

GIS (Geographical Information System) is one of the most striking innovation for mapping applications supplied by the developing computer and software technology to users. GIS is a very effective tool which can show visually combination of the geographical and non-geographical data by recording these to allow interpretations and analysis. DEM (Digital Elevation Model) is an inalienable component of the GIS. The existing TM (Topographic Map) can be used as the main data source for generating DEM by amanual digitizing or vectorization process for the contours polylines. The aim of this study is to examine the DEM accuracies, which were obtained by TMs, as depending on the number of sampling points and grid size. For these purposes, the contours of the several 1/1000 scaled scanned topographical maps were vectorized. The different DEMs of relevant area have been created by using several datasets with different numbers of sampling points. We focused on the DEM creation from contour line...

The problem of maximizing the performance of the detection of ischemia episodes is a difficult pattern classification problem. The state space for this problem consists of regions that lie near class separation boundaries and require the construction of complex discriminants while for the rest regions the classification task is significantly simpler. The motivation for developing the supervising network self-organizing map (sNet-SOM) model is to exploit this fact for designing computationally effective solutions both for the particular ischemic detection problem and for other applications that share similar characteristics. Specifically, the sNet-SOM utilizes unsupervised learning for the "simple" regions and supervised for the "difficult" ones in a two stage learning process. The unsupervised learning approach extends and adapts the self-organizing map (SOM) algorithm of Kohonen. The basic SOM is modified with a dynamic expansion process controlled with an entropy based criterion that allows the adaptive formation of the proper SOM structure. This extension proceeds until the total number of training patterns that are mapped to neurons with high entropy (and therefore with ambiguous classification) reduces to a size manageable numerically with a capable supervised model. The second learning phase (the supervised training) has the objective of constructing better decision boundaries at the ambiguous regions. At this phase, a special supervised network is trained for the computationally reduced task of performing the classification at the ambiguous regions only. The utilization of sNet-SOM with supervised learning based on the radial basis functions and support vector machines has resulted in an improved accuracy of ischemia detection especially in the last case. The highly disciplined design of the generalization performance of the support vector machine allows designing the proper model for the number of patterns transferred to the supervised expert.

Satellite-based information on significant waves is increasingly being made available to ocean scientists and engineers at low costs. While such measurements have a number of useful applications the manner with which the satellites sense the waves limits their applications to nearshore locations. This paper discusses an approach based on the radial basis function (RBF) type of artificial neural networks to map remote-sensed deep-water waves with the coastal waves. Significant wave heights at a number of locations over a track parallel to the coastline are used to estimate the significant wave heights at a nearshore site. The success of the method adopted was confirmed from the satisfactory error measures it produced during the testing carried out following the network training. It was also found that the satellite data need a 'local tuning' as done in the RBF before their further use in network computations. This work also highlighted importance of innovative approaches to calibrate a network on the basis of a given data set.

An investigation to localise facial landmarks from 3D images is presented, without using any assumption concerning facial pose. This paper introduces new surface descriptors, which are derived from either unstructured face data, or a radial basis function (RBF) model of the facial surface. Two new variants of feature descriptors are described, generally named as point - triplet descriptors because they require three vertices to be computed. The first is related to the classical depth map feature, which is referred to as weighted - interpolated depth map. The second variant of descriptors are derived from an implicit RBF model, they are referred to as surface RBF signature (SRS) features. Both variants of descriptors are able to encode surface information within a triangular region defined by a point - triplet into a surface signature, which could be useful not only for 3D face processing but also within a number of graph based retrieval applications. These descriptors are embedded into a system designed to localise the nose - tip and two inner - eye corners. Landmark localisation performance is reported by computing errors of estimated landmark locations against our respective ground --truth data from the Face Recognition Grand Challenge (FRGC) database.

In the near future, autonomous mobile robots are expected to help humans by performing service tasks in many different areas, including personal assistance, transportation, cleaning, mining, or agriculture. In order to manage these tasks in a changing and partially unpredictable environment, without the aid of humans, the robot must have the ability to plan its actions and to execute them robustly and in a safe way. The robot must also have the ability to detect when the execution does not proceed as planned, and to correctly identify the causes of the failure. An execution monitoring system allows the robot to detect and classify these failures.

We present error bounds for the interpolation with anisotropically transformed radial basis functions for both function and its partial derivatives. The bounds rely on a growth function and do not contain unknown constants. For polyharmonic basic functions in R 2 we show that the anisotropic estimates predict a significant improvement of the approximation error if both the target function and the placement of the centres are anisotropic, and this improvement is confirmed numerically.

Most intrusion detection system (IDS) with a single-level structure can only detect either misuse or anomaly attacks. Some IDSs with multi-level structure or multi-classifier are proposed to detect both attacks, but they are limited in adaptively learning. In this paper, two hierarchical IDS frameworks using Radial Basis Functions (RBF) are proposed. A serial hierarchical IDS (SHIDS) is proposed to identify misuse attack accurately and anomaly attacks adaptively. A parallel hierarchical IDS (PHIDS) is proposed to enhance the SHIDSÕs functionalities and performance. The experiments show that the two proposed IDSs can detect network intrusions in real-time, train new classifiers for novel intrusions automatically, and modify their structures adaptively after new classifiers are trained.

An automated approach to degradation analysis is proposed that uses a rotating machine's acoustic signal to determine Remaining Useful Life (RUL). High resolution spectral features are extracted from the acoustic data collected over the entire lifetime of the machine. A novel approach to the computation of Mutual Information based Feature Subset Selection is applied, to remove redundant and irrelevant features, that does not require class label boundaries of the dataset or spectral locations of developing defect to be known or pre-estimated. Using subsets of the feature space, multi-class linear and Radial Basis Function (RBF) Support Vector Machine (SVM) classifiers are developed and a comparison of their performance is provided. Performance of all classifiers is found to be very high, 85 to 98%, with RBF SVMs outperforming linear SVMs when a smaller number of features are used. As larger numbers of features are used for classification, the problem space becomes more linearly separable and the linear SVMs are shown to have comparable performance. A detailed analysis of the misclassifications is provided and an approach to better understand and interpret costly misclassifications is discussed. While defining class label boundaries using an automated k-means clustering algorithm improves performance with an accuracy of approximately 99%, further analysis shows that in 88% of all misclassifications the actual class of failure had the next highest probability of occurring. Thus, a system that incorporates probability distributions as a measure of confidence for the predicted RUL would provide additional valuable information for scheduling preventative maintenance.

Advances in technology have allowed for the improvement of geodetic reference systems (GRSs). Relating different GRSs can be done by employing transformation parameters which may not, however, be satisfactory in certain applications due to the heterogeneous and local character of deformations caused by the procedures adopted in classical networks. Classical networks were established basically by procedures of triangulation and traverse survey, and the existence of these deformations justifies the search for new transformation methodologies. This study evaluated artificial neural networks (ANNs) as a tool for the transformation between GRSs. Frames points with known geodetic coordinates (latitude and longitude) in the South American Datum of 1969 (SAD69) system and in the older Córrego Alegre system, both still in use in Brazil, were chosen for this study. The SAD69 coordinates of the frame points were transformed into Co´rrego Alegre coordinates and then the computed coordinates were compared with known ones. Four tests were carried out in order to transform the coordinates. The first test involved the use of official transformation parameters and the formulas of Molodensky. In the second test, new transformation parameters were employed. In the third test new regional transformation parameters were determined, while the fourth test employed an ANN to predict the Co´rrego Alegre coordinates of the check points. Results indicated that the employment of an ANN transformed the coordinates most accurately, and indicated that they can be useful in modeling deformations in classical networks.

This paper presents a study highlighting the predictive performance of a radial basis function (RBF) network in estimating the grade of an offshore placer gold deposit. In applying the radial basis function network to grade estimation of the deposit, several pertinent issues regarding RBF model construction are addressed in this study. One of the issues is the selection of the RBF network along with its center and width parameters. Selection was done by an evolutionary algorithm that utilizes the concept of cooperative coevolutions of the RBFs and the associated network. Furthermore, the problem of data division, which arose during the creation of the training, calibration and validation of data sets for the RBF model development, was resolved with the help of an integrated approach of data segmentation and genetic algorithms (GA). A simulation study conducted showed that nearly 27% of the time, a bad data division would result if random data divisions were adopted in this study. In addition, the efficacy of the RBF network was tested against a feed-forward network and geostatistical techniques. The outcome of this comparative study indicated that the RBF model performed decisively better than the feed-forward network and the ordinary kriging (OK).

In this paper, a methodology for understanding the relationships between process parameters and the bead area geometry are presented. The objective of the first part of this study is to find the optimal bead area geometry in the Gas Metal Arc Welding (GMAW) process. A radial basis function (RBF) neural network is used for the prediction of the cross sectional area of the welding bead using a three level factorial design of experiments for the training of the neural network.

The local RBF is becoming increasingly popular as an alternative to the global version that suffers from ill-conditioning. In this paper, we study analytically the convergence behavior of the local RBF method as a function of the number of nodes employed in the scheme, the nodal distance, and the shape parameter. We derive exact formulas for the first and second derivatives in one dimension, and for the Laplacian in two dimensions. Using these formulas we compute Taylor expansions for the error. From this analysis, we find that there is an optimal value of the shape parameter for which the error is minimum. This optimal parameter is independent of the nodal distance. Our theoretical results are corroborated by numerical experiments.

Background: Occurrence of protein in the cell is an important step in understanding its function. It is highly desirable to predict a protein's subcellular locations automatically from its sequence. Most studied methods for prediction of subcellular localization of proteins are signal peptides, the location by sequence homology, and the correlation between the total amino acid compositions of proteins. Taking amino-acid composition and amino acid pair composition into consideration helps improving the prediction accuracy.

The objective of voice conversion system is to formulate the mapping function which can transform the source speaker characteristics to that of the target speaker. In this paper, we propose the General Regression Neural Network (GRNN) based model for voice conversion. It is a single pass learning network that makes the training procedure fast and comparatively less time consuming. The proposed system uses the shape of the vocal tract, the shape of the glottal pulse (excitation signal) and long term prosodic features to carry out the voice conversion task. In this paper, the shape of the vocal tract and the shape of source excitation of a particular speaker are represented using Line Spectral Frequencies (LSFs) and Linear Prediction (LP) residual respectively. GRNN is used to obtain the mapping function between the source and target speakers. The direct transformation of the time domain residual using Artificial Neural Network (ANN) causes phase change and generates artifacts in consecutive frames. In order to alleviate it, wavelet packet decomposed coefficients are used to characterize the excitation of the speech signal. The long term prosodic parameters namely, pitch contour (intonation) and the energy profile of the test signal are also modified in relation to that of the target (desired) speaker using the baseline method. The relative performances of the proposed model are compared to voice conversion system based on the state of the art RBF and GMM models using objective and subjective evaluation measures. The evaluation measures show that the proposed GRNN based voice conversion system performs slightly better than the state of the art models.

In this communication, we propose the use of Support Vector Machines (SVM) for crop classification using hyperspectral images. SVM are benchmarked to well-known neural networks such as multilayer perceptrons (MLP), Radial Basis Functions (RBF) and Co-Active Neural Fuzzy Inference Systems (CANFIS). Models are analyzed in terms of efficiency and robustness, which is tested according to their suitability to real-time working conditions whenever a preprocessing stage is not possible. This can be simulated by considering models with and without a preprocessing stage. Four scenarios (128, 6, 3 and 2 bands) are thus evaluated. Several conclusions are drawn: (1) SVM yield better outcomes than neural networks; (2) training neural models is unfeasible when working with high dimensional input spaces and (3) SVM perform similarly in the four classification scenarios, which indicates that noisy bands are successfully detected.

Artificial neural networks ͑ANN͒ are typically composed of a large number of nonlinear functions ͑neurons͒ each with several linear and nonlinear parameters that are fitted to data through a computationally intensive training process. Longer training results in a closer fit to the data, but excessive training will lead to overfitting. We propose an alternative scheme that has previously been described for radial basis functions ͑RBF͒. We show that fundamental differences between ANN and RBF make application of this scheme to ANN nontrivial. Under this scheme, the training process is replaced by an optimal fitting routine, and overfitting is avoided by controlling the number of neurons in the network. We show that for time series modeling and prediction, this procedure leads to small models ͑few neurons͒ that mimic the underlying dynamics of the system well and do not overfit the data. We apply this algorithm to several computational and real systems including chaotic differential equations, the annual sunspot count, and experimental data obtained from a chaotic laser. Our experiments indicate that the structural differences between ANN and RBF make ANN particularly well suited to modeling chaotic time series data.

The eyes are complex sensory organs and are designed to optimize vision under conditions of varying light. There are a number of eye disorders that can influence vision. Eye disorders among the elderly are a major health problem. With advancing age, the normal function of eye tissues decreases and there is an increased incidence of ocular pathology. The most common symptoms elicited from ocular diseases are few in number and non-specific in nature: blurred vision, pain, and redness. Cataracts occur most frequently in older people and have significant impact on an individual's quality of life. There are effective therapies and visual aids for these potential vision-limiting conditions. Corneal haze a complication of refractive surgery is characterized by the cloudiness of the normally clear cornea. Iridocyclitis is the inflammation of the Iris and ciliary body. In corneal arcus are white circles in the cornea of the eye caused by fatty deposits. So, there is a need to diagnose to the normal eye from the abnormal one. This paper presents an identification of normal eye image and abnormal (consists of five kinds of eye images) classes using radial basis function (RBF) classifier. The features are extracted from the raw images using the image processing techniques and fuzzy Kmeans algorithm. Our system uses 150 subjects, consisting of five different kinds of eye disease conditions. We demonstrated a sensitivity of 90%, for the classifier with the specificity of 100%. Our systems are ready clinically to run on large amount of data sets.

In this paper, we have derived a radial basis function (RBF) based method for the pricing of financial contracts by solving the Black–Scholes partial differential equation. As an example of a financial contract that can be priced with this method we have chosen the multi-dimensional European basket call option. We have shown numerically that our scheme is second-order accurate in time and spectrally accurate in space for constant shape parameter. For other non-optimal choices of shape parameter values, the resulting convergence rate is algebraic. We propose an adapted node point placement that improves the accuracy compared with a uniform distribution. Compared with an adaptive finite difference method, the RBF method is 20–40 times faster in one and two space dimensions and has approximately the same memory requirements.

The goal of our project was to implement the Radial-Basis Function Network (RBFN) on three domains of varying sizes, in terms of number of attributes and class labels. In section 2, we discuss how we implemented RBFN. We then explored the UCI repository and restricted the size of each domain dataset to be no larger than a few hundred instances, the details of which will be delineated in section 3. Finally, in section 4 we state our results for each domain, comparing the final testing accuracy by varying total number of hidden neurons and learning rate.

The human face is an elastic object. A natural paradigm for representing facial expressions is to form a complete 3D model of facial muscles and tissues. However, determining the actual parameter values for synthesizing and animating facial expressions is tedious; evaluating these parameters for facial expression analysis out of grey-level images is ahead of the state of the art in computer vision. Using only 2D face images and a small number of anchor points, we show that the method of radial basis functions provides a powerful mechanism for processing facial expressions. Although constructed speci cally for facial expressions, our method is applicable to other elastic objects as well.

Particle swarm optimization (PSO) is a population based optimization technique developed by Dr. Eberhart and Dr. Kennedy in 1995, inspired by social behavior of bird flocking or fish schooling. It is a computational method that optimizes a problem by iteratively trying to improve a candidate solution with regard to a given measure of quality. It is an optimization of continuous nonlinear functions that are used to find the best solution in problem space.. In this paper, this nature inspired behaviour has been considered to optimise the neural network i.e Radial Basis Function by PSO. The RBF is a Neural Network. It is based on moving or directed along the radius. Radial Basis Function emerged as a variant of artificial neural networks in late 80's. RBF's are embedded as two layer neural network, where each hidden unit implements a radial activated function. The output units implement a weighted sum of hidden unit outputs. In order to use a Radial Basis Function Network we ne...

We present a real-time algorithm called compensated ray marching for rendering of smoke under dynamic low-frequency environment lighting. Our approach is based on a decomposition of the input smoke animation, represented as a sequence of volumetric density fields, into a set of radial basis functions (RBFs) and a sequence of residual fields. To expedite rendering, the source radiance distribution within the smoke is computed from only the lowfrequency RBF approximation of the density fields, since the highfrequency residuals have little impact on global illumination under low-frequency environment lighting. Furthermore, in computing source radiances the contributions from single and multiple scattering are evaluated at only the RBF centers and then approximated at other points in the volume using an RBF-based interpolation. A slice-based integration of these source radiances along each view ray is then performed to render the final image. The high-frequency residual fields, which are a critical component in the local appearance of smoke, are compensated back into the radiance integral during this ray march to generate images of high detail. The runtime algorithm, which includes both light transfer simulation and ray marching, can be easily implemented on the GPU, and thus allows for real-time manipulation of viewpoint and lighting, as well as interactive editing of smoke attributes such as extinction cross section, scattering albedo, and phase function. Only moderate preprocessing time and storage is needed. This approach provides the first method for real-time smoke rendering that includes single and multiple scattering while generating results comparable in quality to offline algorithms like ray tracing.

Wave parameters prediction is an important issue in coastal and offshore engineering. In this literature, several models and methods are introduced. In the recent years, the well-known soft computing approaches, such as artificial neural networks, fuzzy and adaptive neuro-fuzzy inference systems and etc., have been known as novel methods to form intelligent systems, these approaches has also been used to predict wave parameters, as well. It is not a long time that support vector machine (SVM) is introduced as a strong machine learning and data mining tool. In this paper, it is used to predict significant wave height (H s ). The data set used in this study comprises wave wind data gathered from deep water locations in Lake Michigan. Current wind speed (u) and those belonging up to six previous hours are given as input variables, while the significant wave height is the output parameter. The SVM results are compared with those of artificial neural networks, multi-layer perceptron (MLP) and radial basis function (RBF) models. The results show that SVM can be successfully used for prediction of H s . Furthermore, comparisons indicate that the error statistics of SVM model marginally outperforms ANN even with much less computational time required.

In this paper, we solve the customer credit card churn prediction via data mining. We developed an ensemble system incorporating majority voting and involving Multilayer Perceptron (MLP), Logistic Regression (LR), decision trees (J48), Random Forest (RF), Radial Basis Function (RBF) network and Support Vector Machine (SVM) as the constituents. The dataset was taken from the Business Intelligence Cup organised by the University of Chile in 2004. Since it is a highly unbalanced dataset with 93% loyal and 7% churned customers, we employed (1) undersampling, (2) oversampling, (3) a combination of undersampling and oversampling and (4) the Synthetic Minority Oversampling Technique (SMOTE) for balancing it. Furthermore, tenfold cross-validation was employed. The results indicated that SMOTE achieved good overall accuracy. Also, SMOTE and a combination of undersampling and oversampling improved the sensitivity and overall accuracy in majority voting. In addition, the Classification and Regression Tree (CART) was used for the purpose of feature selection. The reduced feature set was fed to the classifiers mentioned above. Thus, this paper outlines the most important predictor variables in solving the credit card churn prediction problem. Moreover, the rules generated by decision tree J48 act as an early warning expert system.

This paper describes a GIS-based application of a radial basis functional link net (RBFLN) to map the potential of SEDEX-type base metal deposits in a study area in the Aravalli metallogenic province (western India). Available public domain geodata of the study area were processed to generate evidential maps, which subsequently were encoded and combined to derive a set of input feature vectors. A subset of feature vectors with known targets (i.e., either known mineralized or known barren locations) was extracted and divided into (a) a training data set and (b) a validation data set. A series of RBFLNs were trained to determine the network architecture and estimate parameters that mapped the maximum number of validation vectors correctly to their respective targets. The trained RBFLN that gave the best performance for the validation data set was used for processing all feature vectors. The output for each feature vector is a predictive value between 1 and 0, indicating the extent to which a feature vector belongs to either the mineralized or the barren class. These values were mapped to generate a predictive classification map, which was reclassified into a favorability map showing zones with high, moderate and low favorability for SEDEX-type base metal deposits in the study area. The method demarcates successfully high favorability zones, which occupy 6% of the study area and contain 94% of the known base metal deposits.

Face Expression Recognition is very fast growing research field in computer vision & artificial intelligence. Human Facial Expression is not just an easy and straightforward task due to several circumstances like illumination, facial occlusions, face shape/colour etc. Its applications include human-computer interfaces, human emotion analysis, and medical care and cure. The paper deals with the comparative study of neural network based approaches with its application to the facial expression recognition system.

Linear systems of equations and their reliable solution is a key part of nearly all computational systems and in a solution of many engineering problems. Mostly, the estimation of the matrix conditionality is used for an assessment of the solvability of linear systems, which are important for interpolation, approximation , and solution of partial differential equations especially for large data sets with large range of values. In this contribution, a new approach to the matrix conditionality and the solvabil-ity of the linear systems of equations is presented. It is based on the application of the geometric algebra with the projective space representation using homogeneous coordinates representation. However, the physical floating-point representation , mostly the IEEE 754-219, has to be strictly respected as many algorithms fail due to this.

""This paper presents an application of the
techniques of Artificial Intelligence (AI) in the medical
diagnostic. It showed as alternative to work an Artificial
Neuronal Network of Basis Radial Function (RBF) modified, it
is applied as Fuzzy Classifier. To establish a comparison was
implemented the same system with neuronal networks type
Multilayer Perceptron MLP and, also it was compared with
results of classification methods reported in the literature
based on Fuzzy Clustering with Fuzzy C-Means (FCM).
Taking the databases of Wisconsin Breast Cancer of the UCI
repository was implemented the diagnostic of patients with
benign tumors or not. The programming is developed through
software MATLAB. The results with RBF as fuzzy classifier
allowed to obtain that this alternative is obtained a good
classifier with a low margin of error, and a good performance
in the generalization compared with the others methods.

Este artículo presenta una aplicación de las
técnicas de Inteligencia Artificial (IA) en el diagnóstico
médico. Se presenta una alternativa para trabajar una Red
Neuronal Artificial de Función de Base Radial (RBF)
modificada para ser aplicada como Clasificador Difuso. Para
establecer una comparación se implementó el mismo sistema
con redes neuronales tipo Perceptrón Multicapa MLP y,
también se comparó con resultados de métodos de clasificación
reportados en la literatura basados en Clustering Difuso como
Fuzzy C-Means (FCM). Tomando la base de datos del Cáncer
de Seno de Wisconsin del repositorio de la UCI se implementó
el diagnóstico de pacientes con tumores benignos o no. La
programación es desarrollada por medio del software
MATLAB. Los resultados logrados con la RBF como
clasificador difuso permiten evidenciar que con esta
alternativa se obtiene un buen clasificador con un bajo
margen de error y con un buen desempeño en la
generalización comparado con los otros métodos.""

A novel type of learning machine called support vector machine (SVM) has been receiving increasing interest in areas ranging from its original application in pattern recognition to other applications such as regression estimation due to its remarkable generalization performance. This paper deals with the application of SVM in financial time series forecasting. The feasibility of applying SVM in financial forecasting is first examined by comparing it with the multilayer back-propagation (BP) neural network and the regularized radial basis function (RBF) neural network. The variability in performance of SVM with respect to the free parameters is investigated experimentally. Adaptive parameters are then proposed by incorporating the nonstationarity of financial time series into SVM. Five real futures contracts collated from the Chicago Mercantile Market are used as the data sets. The simulation shows that among the three methods, SVM outperforms the BP neural network in financial forecasting, and there are comparable generalization performance between SVM and the regularized RBF neural network. Furthermore, the free parameters of SVM have a great effect on the generalization performance. SVM with adaptive parameters can both achieve higher generalization performance and use fewer support vectors than the standard SVM in financial forecasting.

Nous proposons une méthode d'approximation de fonction par réseaux à fonctions radiales de base. Nous montrerons que cette méthode d'approximation peut être améliorée par un prétraitement des entrées basé sur un modèle linéaire. Cette méthode d'approximation sera appliquée à la détermination du prix d'achat d'une option. Abstract: APROXIMATION USING RADIAL BASIS FUNCTION NETWORKS: APPLICATION TO PRICING DERIVATIVE SECURITIES.

This paper presents a new hybrid optimization strategy for training feedforward neural networks. The algorithm combines gradient-based optimization of nonlinear weights with singular value decomposition (SVD) computation of linear weights in one integrated routine. It is described for the multilayer perceptron (MLP) and radial basis function (RBF) networks and then extended to the local model network (LMN), a new feedforward structure in which a global nonlinear model is constructed from a set of locally valid submodels. Simulation results are presented demonstrating the superiority of the new hybrid training scheme compared to second-order gradient methods. It is particularly effective for the LMN architecture where the linear to nonlinear parameter ratio is large.

Image morphing has been the subject of much attention in recent years. It has proven to be a powerful visual effects tool in film and television, depicting the fluid transformation of one digital image into another. This paper reviews the growth of this field and describes recent advances in image morphing in terms of three areas: feature specification, warp generation methods, and transition control. These areas relate to the ease of use and quality of results. We will describe the role of radial basis functions, thin plate splines, energy minimization, and multilevel free-form deformations in advancing the state-of-the-art in image morphing. Recent work on a generalized framework for morphing among multiple images will be described.

Radial Basis Function (RBF) interpolation is a common approach to scattered data interpolation. Gaussian Process regression is also a common approach to estimating statistical data. Both techniques play a central role, for example, in statistical or machine learning, and recently they have been increasingly applied in other fields such as computer graphics. In this survey we describe the formulation of both techniques as instances of functional regression in a Reproducing Kernel Hilbert Space. We then show that the RBF and Gaussian Process techniques can in some cases be reduced to an identical formulation, differing primarily in their assumptions on when the data locations and values are known, as well as in their (respectively) deterministic and stochastic perspectives. The scope and effectiveness of the RBF and Gaussian process techniques are illustrated through several applications in computer graphics.

A numerical method is developed to solve the nonlinear one-dimensional Klein-Gordon equation by using the cubic B-spline collocation method on the uniform mesh points. We solve the problem for both Dirichlet and Neumann boundary conditions. The convergence and stability of the method are proved. The method is applied on some test examples, and the numerical results have been compared with the exact solutions. The L 2 , L ∞ and Root-Mean-Square errors (RMS) in the solutions show the efficiency of the method computationally.

This paper presents an application of the Radial Basis Function Neural Network (RBFNN)-based identification of an essential oil extraction using Non-Linear Autoregressive Model with Exogenous Inputs (NARX) model. The dataset consisted of a Pseudo-Random Binary Sequence (PRBS) inputs as the control signal, and outputs depicting temperatures inside the distillation column. One Step Ahead (OSA) model fitting and residual tests demonstrated that the RBFNN-based NARX model was able to approximate the system well, while satisfying all validation criterias.

This paper investigates the prediction of a Lorenz chaotic attractor having relatively high values of Lypunov's exponents. The characteristic of this time series is its rich chaotic behavior. For such dynamic reconstruction problem, regularized radial basis function (RBF) neural network (NN) models have been widely employed in the literature. However, author recommends using a two-layer multi-layer perceptron (MLP) NN-based recurrent model. When none of the available linear models have been able to learn the dynamics of this attractor, it is shown that the proposed NN-based auto regressive (AR) and auto regressive moving average (ARMA) models with regularization have not only learned the true trajectory of this attractor, but also performed much better in multi-step-ahead predictions. However, equivalent linear models seem to fail miserably in learning the dynamics of the time series, despite the low values of Akaike's final prediction error (FPE) estimate. Author proposes to employ the recurrent NN-based ARMA model with regularization which clearly outperforms all other models and thus, it is possible to obtain good results for prediction and reconstruction of the dynamics of the chaotic time series with NN-based models.